Staff-wide meetings for Hannity are unusual and one person close to his show expressed surprise because “Hannity doesn’t do meetings.”

But at the meeting held Tuesday afternoon, the anchor told his staff that he's not negotiating an exit despite reports, according to a person present at the meeting. He thanked his staff for what they do and told them he's "always available" to answer questions.

"And don't believe the destroy-Trump media," the person said he added.

According to multiple sources, Hannity has a "key man clause" in his contract that gives him the option of leaving Fox News at any time after the departure of Ailes; he only needs to give 60 days notice before he can leave the network.

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Shine resigned on Monday as the network faces a number of sexual harassment and racial discrimination suits. (Shine is named in some of the lawsuits as someone who was aware of sexual harassment but did not act; he denies wrongdoing.) His resignation follows the ousting of primetime anchor Bill O'Reilly last month and Ailes last year as they faced sexual harassment allegations. Star anchors Megyn Kelly and Greta Van Susteren also left the network in the past year and the network's primetime line up has been completely reworked.